Partial wave expansion of the Coulomb-distorted plane wave is determined and studied. Dominant and sub-dominant asymptotic expansion terms are given and leading order three-dimensional asymptotic form is derived. The generalized hypergeometric functi
on $_2F_2(a,a;a+l+1,a-l;z)$ is expressed with the help of confluent hypergeometric functions and the asymptotic expansion of $_2F_2(a,a;a+l+1,a-l;z)$ is simplified.
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified plane wave
is considered. This decomposition leads a three-dimensional Schrodinger equation with source term. Partial wave expansion is carried out and the asymptotic form of the solution is determined. This splitting does not lead to simplification of the scattering boundary condition if complex scaling is invoked. A new splitting carried out only on partial wave level is introduced and this method is proved to be very useful. The scattered part of the wave function tends to zero at large inter-particle distance. This property permits of easy numerical solution: the scattered part of the wave function can be expanded on bound-state type basis. The new method can be applied not only for pure Coulomb potential butin the presence of short range interaction too.
